With t-channel ρ, f 2(1270) exchange and the ππ→ ρρ→ ππ box diagram contribution, we reproduce the ππ isotensor S-wave and D-wave scattering phase shifts and inelasticities up to 2.2 GeV quite well in a K-matrix formalism. The t-channel ρ exchange provides repulsive negative phase shifts while the t-channel f 2(1270) gives an attractive force to increase the phase shifts for ππ scattering above 1 GeV, and the coupled-channel box diagram causes the inelasticities. The implication to the isoscalar ππ S-wave interaction is discussed.